Beta Decay Studies in nuclear structure

Transcription

1 Beta Decay Studies in nuclear structure Escuela de doctorado de Física Nuclear Santiago 1 de Marzo de 2007 Introducción Cómo hacer una medida Un ejemplo Berta Rubio IFIC (CSIC-Univ. Valencia) B. Rubio. Escuela Doctorado FN, Santiago 2007

2 Most unstable nuclei decay by either β + or β - decay Proton Drip Line 265 stable About 3000 out of 6000 synthesised in our laboratories, only about 100 fission Fission B. Rubio. Escuela Doctorado FN, Santiago 2007 Neutron Drip Line

3 There are two ways (mainly) to study nuclei, reactions and decay Reactions have the advantage of the flexibility, Decay is God given but it is very selective and can Bring us very far from stability B. Rubio. Escuela Doctorado FN, Santiago 2007

4 Typical constants Pion-nucleon ( strong ) 1 Electromagnetic 10-2 β decay ( weak ) 10-5 Gravitational Weak process p Introduction: what is β decay? n W- e- u ν e d W- e- B. Rubio. Escuela Doctorado FN, Santiago 2007 ν e

5 Test of the standard model: yes but only when we can eliminate the nuclear structure factor. But we are not so much concerned with The weak force but rather with the beta decay and nuclear structure Something to remember: because of the weak interaction beta Half-lives are long As soon as particle emission is possible, it will dominate B. Rubio. Escuela Doctorado FN, Santiago 2007

6 Far of stability beta decay is often the first piece of information we encounter: Few atoms per day: Existence Half life (even an inaccurate number) Mass (even an inaccurate number) Some atoms per second Spin, excited states 100 to 1000 atoms per second Full or very complete spectroscopy B. Rubio. Escuela Doctorado FN, Santiago 2007

7 i f proton neutron B. Rubio. Escuela Doctorado FN, Santiago 2007

8 The real process β - : n p + e - + ν β + : p n + e + + ν EC : p + e- n + ν Always in competition with β + β - : In real nuclei A Z X N A X Z + 1 N 1 + e + ν e ß+ β + : A Z X N A X Z 1 N e + + ν e ß- EC : A Z A X + e + ν N N e + Z X X ray B. Rubio. Escuela Doctorado FN, Santiago 2007

9 B. Rubio. Escuela Doctorado FN, Santiago 2007 ) ( ) ( e N N X X N A Z N A Z ) ( ) ( e N N X X N A Z N A Z β - : β + : ) ( ) ( 1 1 X X N A Z N A Z e N + + EC : The β decay Q-value N=nuclear masses If we use atomic masses!!! Q β - = Q β + = Q EC = [ ] ) ( ) ( c M M X X N A Z N A Z + [ ] ) ( ) ( c m c M M e N A Z N A Z X X + [ ] e N A Z N A Z B c M M X X ) ( ) ( (Normally the mass excess is used- Audi tables)

10 I = 0,1 Quantum numbers and the selection rules for allowed β-decay l s = π = r r r r Ii = I f + s( e ) + s( ν ) r v r r r I = Ii I f = s( e ) + s( ν ) r r r r I = L + s = s = 0 0,1 0 Selection rules 0 + to 0 + Gamow Teller forbidden!!! B. Rubio. Escuela Doctorado FN, Santiago 2007 e - e - ν ν Single state, Fermi Triplet state Gamow Teller

11 The operator responsible for the process στ στ Gamow-Teller Or τ Fermi 28 2 p 1/2 1 f 5/2 2 p 3/2 1 f 7/2 στ 28 1 f 5/2 2 p 3/2 1 f 7/2 τ B. Rubio. Escuela Doctorado FN, Santiago 2007

12 The isospin formalism: p and n are the same kind of particles with a different isospin state (T) The third component T z is very clear: T Z N Z = 2 τ Fermi Can only change the third component of isospin: Only one state called Isobaric Analog State (IAS) στ στ Gamow-Teller Can change the spin and the isospin: Many possible final states B. Rubio. Escuela Doctorado FN, Santiago 2007

13 Fermi transitions Kr 38 T T Z =1 =1 T=8 T Z = Rb 51 β - β Br 39 T 1, T = T Z = 2 2 T=8 T Z = Kr 52 In β + Fermi, forbidden for N>Z In β - allowed but energetically difficult B. Rubio. Escuela Doctorado FN, Santiago 2007

14 Gamow Teller transitions Kr 38 T T Z =1 =1 T=8 T Z = Rb 51 β - β Br 39 T Z T = 2 = 2 T=8 T Z = Kr 52 In β + Gamow Teller allowed In β - Gamow Teller allowed B. Rubio. Escuela Doctorado FN, Santiago 2007

15 The β+ process is hindered due to the occupation Л ν β+ B. Rubio. Escuela Doctorado FN, Santiago 2007

16 Not a problem on the β- side Л ν β- B. Rubio. Escuela Doctorado FN, Santiago 2007

17 Transition probability i τ στ f BF = ψ f τ ± ψ i 2 BGT = ψ f στ ± ψ i 2 B GT and B F can be calculated using microscopic models!!! This is the main message of this talk!!!! B. Rubio. Escuela Doctorado FN, Santiago 2007

18 We will learn in the next lectures how to MEASURE the B GT or B F,, but before that two comments. B. Rubio. Escuela Doctorado FN, Santiago 2007

19 The Ikeda sum rule: MODEL INDEPENDENT π ν S - -S + =B GT- -B GT+ =3(N-Z) β- B GT- (p,n) B GT+ (n,p) In principle β- decay is more interesting because most of the nuclei have more neutrons than protons, and then most of the Ikeda sum rule in the β- side. B. Rubio. Escuela Doctorado FN, Santiago 2007

20 Before we go to the experimental techniques, one word about charge exchange reactions B. Rubio. Escuela Doctorado FN, Santiago 2007

21 Charge exchange reactions Target Exchange of a proton for a neutron Projectile Ejectile The are experimentally very different from the β decay experiments They involve different nuclei The i> state is But they are governed by the same operator!!!!, a and stable are therefore nucleus intimately related B. Rubio. Escuela Doctorado FN, Santiago 2007

22 Two possible explanations: 1232 Higher order configuration mixing: interpretation and normalisation of a reaction spectrum An experimental problem (to analyse the background properly) K.Yako et al CM 2002 B. Rubio. Escuela Doctorado FN, Santiago 2007

23 BGT = ψ f στ ± ψ i 2 BGT = I β ft 1/ 2 B. Rubio. Escuela Doctorado FN, Santiago 2007

24 FIN parte 1 B. Rubio. Escuela Doctorado FN, Santiago 2007

25 Beta decay experiments Production of exotic nuclei, the reaction Separation of the radioactive activity Detection techniques Extraction of the B GT B.Rubio. Es. Doc. Santiago 2007

26 The reaction Any in principle, beta decay will not depend on it B.Rubio. Es. Doc. Santiago 2007

27 In the following example: Isol technique (far from stability: fragmentation in flight technique) B.Rubio. Es. Doc. Santiago 2007

28 Accelerator target Ion source Mass Separator recoil. Time=0 β Z A N γ Time>1 s γ Z-1 A N+1 γ β B.Rubio. Es. Doc. Santiago 2007 Transport system

29 Off beam Projectile Target Fusion evaporation projectile fragmentation, target spallation, fission... n p α n γ γ γ γ ν T1/2=1 s β+ β+ Particle evaporation s Gamma deexcitation fs,ns,µs,ms B.Rubio. Es. Doc. Santiago 2007 Beta-decay ms, s,min,days,years

30 Difference between in beam fusion evaporation and off beam beta decay B.Rubio. Es. Doc. Santiago 2007

31 In beam spectroscopy γ Projectile Target γ γ Ex Information about Yrast or near Yrast states (we can change E and J) I B.Rubio. Es. Doc. Santiago 2007 (D.R.LaFosse et al. P.R.L 78 (1997)614

32 ν β+ Parent Beta Decay: low angular momentum, and high exc. Energy sometimes, but given by nature Ex Daughter Parent β+ Daughter Daughter B.Rubio. Es. Doc. Santiago 2007

33 How to measure the B(GT) Theoretical quantity BGT = ψ f σkτ ± k ψi k 2 Strength function S ( E) β Experimental quantity: = I ( E) β 1 2 f ( Qβ E) T / S β Relationship ± 7 g g 1 E A ( E) = B( GT ) i f 2 B.Rubio. VEs. Doc. E Santiago E 2007 f

34 The Strength Function Beta-feeding S β ( E) = f ( Q β I β ( E) E, Z) T 1/ 2 Fermi function Phase space factor and Coulomb interaction between the β and the nucleus, tabulated, Nuclear Data Tables A10 (1971): Quantities to be measured E= Exc. En. Daugther Q β B.Rubio. Es. Doc. Santiago 2007 β Half life I% ( E) S( E) = = ft 1 ft

35 B.Rubio. Es. Doc. Santiago 2007

36 Q β -measurements, associated to the process Fermi Kurie plot: we measure the maximum energy of the e - B.Rubio. Es. Doc. Santiago 2007

37 Fermi Kurie plot silicon detector to detect electrons Keller et el. NIM A300(1991)67 β B.Rubio. Es. Doc. Santiago 2007

38 But today very precise mass measurements are Possible by other means, and the Q β -value Is calculated as a difference of ground state atomic masses B.Rubio. Es. Doc. Santiago 2007

39 The principle of Penning traps z r 0 0 z0 r A Penning trap can be defined as the superposition of a homogeneous magnetic field and an electrostatic quadrupole field. ω c = Q m B B.Rubio. Es. Doc. Santiago 2007

40 ISOLTRAP, CERN Measurement trap Purification trap RFQ buncher B.Rubio. Es. Doc. Santiago 2007

41 Stopping chamber RFQ buncher Transfer section Purification trap Measurement trap B.Rubio. Es. Doc. Santiago 2007

42 Other methods Mass measurements at storage rings The Euschool Lectures on Physics with Exotic Beams G. F. Bosch Mass measurements at Isolde with Mistral Lunney D, Pearson JM, Thibault C Recent trends in the determination of nuclear masses REVIEWS OF MODERN PHYSICS 75 (3): JUL 2003 B.Rubio. Es. Doc. Santiago 2007

43 dn/dt Half life measurement Z A N β N( t) = N 0 e λt dnγ/dt γ Z-1 A N+1 1 λ = τ = Ln2 T 1/ 2 Nγ t t t t t t

44 Ln( Nγ/ t) A Very simple!!!! A/2 T 1/2 B.Rubio. Es. Doc. Santiago 2007 t

45 Z A N β+? γ γ Beta-feeding Impossible We have to use the gamma Z-1 A N+1 γ1 γ2 B.Rubio. Es. Doc. Santiago 2007

46 B.Rubio. Es. Doc. Santiago 2007 The CLUSTERCUBE A set-up of six EUROBALL CLUSTER detectors at GSI

47 B.Rubio. Es. Doc. Santiago 2007 EXOGAM, GANIL

48 1 - states SINGLES 0+ B.Rubio. Es. Doc. Santiago 2007

49 The Pandemonium problem B.Rubio. Es. Doc. Santiago 2007

50 Beta-feeding far from stability B( GT ) = ψ σ τ ± f k k ψi στ k 2 2 Q β Many states, daughter One state (g.s) parent ψ f ψ f ψ f ψ f ψ f B.Rubio. Es. Doc. Santiago 2007 Further from stability, higher Q β -values

51 For high Q-values, Ge detectors Traditionally fail to detect γ1 γ2 β-feeding at high Z A N excitation energy!!! Z A N B.Rubio. Es. Doc. Santiago 2007

52 We use Ge detectors to construct the decay scheme From the γ-balance we stract the β -feeding What happens if we miss some gamma intensity??? B.Rubio. Es. Doc. Santiago 2007

53 Z A N B.Rubio. Es. Doc. Santiago 2007 β-feeding Aparent β-feeding!!!!!!!!!!

54 Total Absorption spectroscopy γ1 NaI β feeding γ2 γ1 E 2 E 1 γ2 N I β Ideal case B.Rubio. Es. Doc. Santiago 2007 E 2 Ex in the daughter

55 If the case is not ideal: One has to solve the following equation: d R i j = max j= 1 ij f j d i i j E j B.Rubio. Es. Doc. Santiago 2007

56 B.Rubio. Es. Doc. Santiago 2007 TAS at the dead On-line Mass separator at GSI

57 Lucrecia, the TAGS spectrometer at ISOLDE NaI crystal + ancillary detetcors (Ge for X-ray, plastic for β 38 cm x 38 cm B.Rubio. Es. Doc. Santiago 2007

58 FIN parte 2 B.Rubio. Es. Doc. Santiago 2007

59 The deformation of the N=Z nucleus 76 Sr in its ground state Physics motivation Production and separation of 76 Sr activity Experimental set-up Raw data Analysis of the data Final results and interpretation ED Santiago 2007

60 The shape of a nucleus and the concept of deformation ED Santiago 2007

61 The Shape of the nucleus Near closed shells: spherical g 9/2 ED Santiago 2007

62 When we depart from closed shells, the simplest deformation is quadrupole deformation R ( θ, φ ) = R 0 (1 + β 2Y 20 ( θ, φ )) [413]7/ g p f p f s d 9/2 [301]3/2 [301]1/2 (MeV) 0 [422]5/2 1/2 5/2 3/2 28 7/2 20 1/2 3/2 ED -0.4 Santiago [404]9/2 [303]5/ [431]3/2 [440]1/2 [312]3/2-5 [310]1/2 30 [321]1/2 [303]7/2 [312]5/2-10 [321]3/2 [330]1/2 [200]1/2 [202]3/2 [211]1/2-15 ε 0.95 β 2

63 How to measure the deformation B(E2): E2( ) E2(4+ 2+)- E2(2+ 0+) Or to measure the electrical quadrupole moment, By interaction with external gradient electric field, not for even even ED Santiago 2007

64 Static quadrupole moment measurements Finite range droplet model Q 3 β2 + 5π = ZR0 5/ π β 2 S.Raman et al At. Dat and Nucl. Dat. Tables 78 (2001) Not for even-even and not very far from stability ED Santiago 2007

65 B(E2) g.s B(E2) measurements γ-half-life τ γ ( ) [ ] α = E B( E2) / e 1 = τ b The model dependent relationship with deformation: [ ] 2 B( E2) 1/ 2 β = ( 4π / 3ZR e 2 0 ) / S.Raman et al At. Dat and Nucl. Dat. Tables 78 (2001) ED Santiago 2007 Other experiments like Electron Scat., Coulomb exc. Difficult far of stability

66 Future: Coulomb excitation: REX-Isolde, GANIL Electron scattering: FAIR, GSI ED Santiago 2007

67 Far from stability: level spacing E = E2(4+ 2+)- E2(2+ 0+) n γ E h E The empirical (2) 2 J dynamic = Grodzin s formula β 2 J A 7 /3 E + 1/ 2 = 2 5 AMR 2 1 (2 β cos( ) O θ + 120º ) 5 4π For axially symmetric rotor θ=90º E γ ED Santiago 2007

68 However, none of these methods will give us the sign of the deformation [413]7/ ED Santiago g p f p f s d 9/2 [301]3/2 [301]1/2 (MeV) 0 [422]5/2 1/2 5/2 3/2 28 7/2 20 1/2 3/2 40 [404]9/2 [303]5/ [431]3/2 [440]1/2 [312]3/2-5 [310]1/2 30 [321]1/2 [303]7/2 [312]5/2-10 [321]3/2 [330]1/2 [200]1/2 [202]3/2 [211]1/2-15 OBLATE ε 0.95 β 2 PROLATE

69 In this context, the N Z region around mass 70 is particularly interesting Strong oblateprolate competition Why? Strong def. Rapid shape transitions Shape mixing (MeV) [404]9/2 [211]1/2 g p 38 f p f s d 9/2 1/2 5/2 3/2 28 7/2 20 1/2 3/2 [303]5/2 [413]7/2 [301]1/2 [312]3/2 [321]1/2 [303]7/2 [312]5/2 [321]3/2 [330]1/2 [200]1/2 [440]1/2 [310]1/2 [202]3/2 [301]3/2 [431]3/ [422]5/2 30 Oblate ED Santiago 2007 Prolate

70 Strong deformation Ref. Gelletly et al P.L.B253 (1991)287 ED Santiago 2007

71 The sign of the deformation??? ED Santiago 2007

72 Can beta decay help to solve this problem? BGT = ψ στ ± f ψ i 2 First idea, Hamamoto and collaborators Def HF +BCS+TDA [I. Hamamoto et al., Z. Phys. A353 (1995) 145] Further pursued by Sarriguren and collaborators Def HF+BCS+QRPA [P. Sarriguren et al., Nuc. Phys. A635 (1999) 13] ED Santiago 2007

73 In N~Z nuclei Protons and neutrons occupy partially the same orbitals Gamow-Teller decay allowed. large part of the GT strength inside the Q EC window ED Santiago 2007

74 Here we see the B GT distribution for Sr nuclei Q β Sarriguren ED Santiago 2007

75 We want to measure the beta decay of 76Sr ED Santiago 2007

76 Isolde at CERN ED Santiago 2007

77 ED Santiago 2007

78 In general not all of them used!!! 2.4 µ s 1.2 s (...) ED Santiago s

79 Reaction: 1.4 GeV protons on 52g/cm 2 Nb, surface ionisation Fluorination technique. M/ M=5000 Lucrecia ED Santiago 2007

80 Shielding Polyethylene Lead Copper Aluminium Factor 6 ED Santiago 2007

81 Lucrecia, the TAGS spectrometer at ISOLDE NaI crystal + ancillary detectors (Ge for X-ray, plastic for β ) 38 cm x 38 cm ED Santiago 2007

82 Ancillary Detectors The plastic β detector X-ray detector Tape transport system ED Santiago 2007

83 Efficiency of the Total Absorption Gamma Spectrometer Lucrecia Efficiency Total Efficiency Peak Efficiency ED Santiago 2007 Energy (kev)

84 About 5000 counts/s of 76Sr Symmetric cycle of 15 s (T 1/2 76Sr=9s, T 1/2 76Rb 36.8 s) Counts Counts Counts Lucrecia 10 4 Singles kev ( ) kev ( ) kev Energy (kev) Beta Beta detector Gated Channel X-ray Gated X-ray detector ED 8000 Santiago Q EC =6240 kev Energy (kev) 76Sr activity 76Rb activity Background (1500 counts/s, intrinsic) Pile up 76 Sr + 76 Rb β + 76 Sr EC

85 Geant simulation The 24 Na source, also produced at Isolde At the same position 4123keV 1369keV 2754keV Black: measured source Red: Simulation with GEANT4 ED Santiago 2007

86 Analysis We can use the EM algorithm to calculate the feedigs But we need to assume the levels and the way they decay: Known high resolution level scheme, statistical model Statistical model High res. Data Dessagne et al EPJA20(2004)405 ED Santiago 2007

87 After 300 iterations. ED Santiago 2007

88 Results of of 76 Sr Sr β-decay Counts I β Energy (MeV) Experiment Energy (MeV) Energy (MeV) The β feeding B(GT) (g A 2 /4π) B(GT) (g A 2 /4π) Recalculated ED Santiago β-delayed gamma-rays (this work) β-delayed protons (Dessagne et al.) Energy (MeV)

89 Comparison High Resolution versus Total Absorption I β (%) B(GT)(g A 2 /4π) Q EC =6240 kev ED Santiago 2007 Energy (kev)

90 Results of of 76 Sr Sr β-decay: clearly prolate!!! ΣB(GT) (g A 2 /4π) 5 4 Theo.prolate Theo.oblate ( ) E.Nácher PRL 92 (2004) Sr 3 2 Oblate 1 Prolate Q EC Energy (MeV) ( ) P.Sarriguren et al.npa 658 (1999)13 Strong deformation in ED agreement Santiago 2007with [C.J. Lister Phys.. Rev. C 42 (1990) R1191], but now we have the sign Lister et al.,

91 74 Kr, shape admixture 76 Sr clearly prolate 74 Kr ΣB(GT) (g A 2 /4π) Theo.prolate Theo.oblate E.Nácher PRL 92 (2004) ( ) 76 Sr 2 Oblate E.Poirier PRC 69 (2004) , agreement with in beam studies. 1 Prolate Q EC ED Santiago 2007 Energy (MeV) ( ) P.Sarriguren et al.npa 658 (1999)13

92 FIN ED Santiago 2007